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Mahlaba, Sfiso Cebolenkosi – For the Learning of Mathematics, 2020

Mathematics in its nature is exploratory, giving learners a chance to view it from different perspectives. However, during most of their schooling, South African learners are rarely exposed to mathematical explorations, either because of the lack of resources or the nature of the curriculum in use. Perhaps, this is due to teachers' inability to…

Descriptors: Geometry, Logical Thinking, Mathematical Logic, Validity

Jungic, Veselin; Yan, Xiaoheng – For the Learning of Mathematics, 2020

The aim of this article is to advise readers that natural numbers may be introduced as ordinal numbers or cardinal numbers and that there is an ongoing discussion about which come first. In addition, through several examples, the authors demonstrate that in the process of answering the question "How many?" one may, if convenient, use…

Descriptors: Number Concepts, Mathematics Instruction, Cognitive Processes, Numbers

Adiredja, Aditya P.; Louie, Nicole – For the Learning of Mathematics, 2020

Despite advances toward equity, mathematics education continues to be entangled with deficit discourses at every level. Here, we analyze the webs of meaning that comprise deficit discourses. We show how these discourses are supported by seemingly neutral narratives about what counts as mathematics and narratives about students from marginalized…

Descriptors: Mathematics Education, Equal Education, Social Bias, At Risk Students

Faustino, Ana Carolina; Skovsmose, Ole – For the Learning of Mathematics, 2020

Dialogue has been characterised as a communicative pattern that supports critical learning in education. Seeking to analyse this relationship, we investigated the interaction between teachers and students in two classes, a Third Grade and a Fifth Grade of São Paulo State public school. During the interaction, we identified a variety of dialogic…

Descriptors: Mathematics Instruction, Teaching Methods, Dialogs (Language), Interpersonal Communication

Staples, Megan; Lesseig, Kristin – For the Learning of Mathematics, 2020

Mathematical argumentation, justification, and proof are practices at the heart of mathematics. Yet mathematics teachers generally operate without clear definitions of these practices making it difficult to communicate expectations, decide what to accept or expect from students at different grade levels, and distinguish these activities from…

Descriptors: Mathematics Instruction, Teacher Attitudes, Learning Activities, Mathematics Teachers

Pinto, Alon; Karsenty, Ronnie – For the Learning of Mathematics, 2020

While proof is often presented to mathematics undergraduates as a well-defined mathematical object, the proofs students encounter in different pedagogical contexts may bear salient differences. In this paper we draw on the work of Dawkins and Weber (2017) to explore variations in norms and values underlying a proof across different pedagogical…

Descriptors: Validity, Mathematical Logic, Undergraduate Study, College Mathematics

Maffia, Andrea; Sabena, Cristina – For the Learning of Mathematics, 2020

Literature has already shown that gestures play a relevant role in classroom interactions between students and teacher. We integrate the perspective of Theory of Semiotic Mediation with the notion of Semiotic Bundle to illustrate how gestures can be used as "pivot signs" in semiotic chains. This means that gestures can be performed by…

Descriptors: Mathematics Teachers, Teaching Methods, Nonverbal Communication, Mathematical Concepts

Skovsmose, Ole – For the Learning of Mathematics, 2020

The article identifies three narratives about mathematics education. The first claims that mathematics is a wonderful subject, which provides a true foundation for human knowledge and progress. The second presents mathematics as a suspicious subject, which serves functions of oppression. The third highlights that mathematics has critical…

Descriptors: Mathematics Education, Social Influences, Mathematics, Political Issues

Melhuish, Kathleen; Czocher, Jennifer A. – For the Learning of Mathematics, 2020

Within a study of student reasoning in abstract algebra, we encountered the claim "division and multiplication are the same operation." What might prompt a student to make this claim? What kind of influence might believing it have on their mathematical development? We explored the philosophical roots of "sameness" claims to…

Descriptors: Mathematics Instruction, Elementary Secondary Education, Algebra, Multiplication

Mesa, Vilma; Mali, Angeliki – For the Learning of Mathematics, 2020

We reflect on the evolution of an instrument designed to gather data about student actions with dynamic textbooks in university mathematics in a large-scale project. We also discuss the evolution of our understanding of the mediating role of this instrument in gathering data remotely that allow us to access student use and reconstruct their…

Descriptors: Textbooks, Electronic Publishing, College Students, College Mathematics

Gabel, Mika; Dreyfus, Tommy – For the Learning of Mathematics, 2020

In this paper, we discuss the relationship between rhetoric and mathematics, focusing on mathematical proofs. We offer a theoretical framework based on Perelman's New Rhetoric for analyzing the teaching of proof, taking into account rhetorical aspects. We illustrate the practicality and applicability of the proposed framework and methodology by…

Descriptors: Mathematics Instruction, Teaching Methods, Validity, Mathematical Logic

Lee, Hwa Young; Hardison, Hamilton L.; Paoletti, Teo – For the Learning of Mathematics, 2020

Critical to constructing and interpreting graphs is an individual's understanding of the underlying coordinate systems, yet coordinate systems are often overlooked or taken-for-granted in both mathematics education research and curricula. In this paper, we foreground coordinate systems and present a distinction between two uses of coordinate…

Descriptors: Mathematics Instruction, Teaching Methods, Visual Aids, Graphs

Walkoe, Janet; Levin, Mariana – For the Learning of Mathematics, 2020

We hypothesize that one thing that has been holding the field back from recognizing the algebraic potential of young children's early experiences is an emphasis on specific definitions of what counts as algebra-relevant knowledge. In this article, we seek to develop a perspective on algebraic thinking that foregrounds the algebraic potential of…

Descriptors: Algebra, Thinking Skills, Mathematics Education, Definitions

Büscher, Christian – For the Learning of Mathematics, 2020

New Artificial Intelligence methods hold the potential to transform qualitative research in mathematics education. This study introduces and uses the machine learning technology of simple neural networks to automatically analyse transcript data. This serves as the basis to reflect on the use of machine learning technology in order to uncover some…

Descriptors: Mathematics Education, Educational Research, Artificial Intelligence, Networks

Niss, Mogens – For the Learning of Mathematics, 2019

The purpose of this paper is to discuss a phenomenon that has evolved in mathematics education research journal articles during the last three decades, namely the 'ideal-typical' research paper. By not reflecting today's multi-faceted reality of the field, the ideal-typical research paper represents a far too narrow and rigid understanding of…

Descriptors: Mathematics Education, Educational Research, Journal Articles, Text Structure